2022年二次函数的最值问题总结 .pdf

二次函数的最值问题二次函数2(0)yaxbxca是初中函数的主要内容，也是高中学习的重要基础在初中阶段大家已经知道：二次函数在自变量x取任意实数时的最值情况(当0a时，函数在2bxa处取得最小值244acba，无最大值；当0a时，函数在2bxa处取得最大值244acba，无最小值本节我们将在这个基础上继续学习当自变量x在某个范围内取值时，函数的最值问题同时还将学习二次函数的最值问题在实际生活中的简单应用二次函数求最值（一般范围类）例 1当22x时，求函数223yxx的最大值和最小值分析：作出函数在所给范围的及其对称轴的草图，观察图象的最高点和最低点，由此得到函数的最大值、最小值及函数取到最值时相应自变量x的值解：作出函数的图象当1x时，min4y，当2x时，max5y例 2当12x时，求函数21yxx的最大值和最小值解：作出函数的图象当1x时，min1y，当2x时，max5y由上述两例可以看到，二次函数在自变量x的给定范围内，对应的图象是抛物线上的一段那么最高点的纵坐标即为函数的最大值，最低点的纵坐标即为函数的最小值根据二次函数对称轴的位置，函数在所给自变量x的范围的图象形状各异下面给出一些常见情况：例 3当0 x时，求函数(2)yxx的取值范围解：作出函数2(2)2yxxxx在0 x内的图象可以看出：当1x时，min1y，无最大值所以，当0 x时，函数的取值范围是1y例 4当1txt时，求函数21522yxx的最小值(其中t为常数)分析：由于x所给的范围随着t的变化而变化，所以需要比较对称轴与其范围的相对位置解：函数21522yxx的对称轴为1x画出其草图(1)当对称轴在所给范围左侧即1t时：当xt时，2min1522ytt；(2)当对称轴在所给范围之间即1101ttt时：当1x时，2min1511322y；(3)当对称轴在所给范围右侧即110tt时：当1xt时，22min151(1)(1)3222yttt综上所述：2213,023,0115,122ttytttt在实际生活中，我们也会遇到一些与二次函数有关的问题：二次函数求最值(经济类问题)例 1为了扩大内需，让惠于农民，丰富农民的业余生活，鼓励送彩电下乡，国家决定对购买彩电的农户实行政府补贴规定每购买一台彩电，政府补贴若干元，经调查某商场销售彩电台数y（台）与补贴款额x（元）之间大致满足如图所示的一次函数关系随着补贴款额x的不断增大，销售量也不断增加，但每台彩电的收益Z（元）会相应降低且Z与x之间也大致满足如图所示的一次函数关系文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8（1）在政府未出台补贴措施前，该商场销售彩电的总收益额为多少元？（2）在政府补贴政策实施后，分别求出该商场销售彩电台数y和每台家电的收益Z与政府补贴款额x之间的函数关系式；（3）要使该商场销售彩电的总收益w（元）最大，政府应将每台补贴款额x定为多少？并求出总收益w的最大值分析：（1）政府未出台补贴措施前，商场销售彩电台数为800 台，每台彩电的收益为200 元；（2）利用两个图像中提供的点的坐标求各自的解析式；（3）商场销售彩电的总收益商场销售彩电台数每台家电的收益，将（2）中的关系式代入得到二次函数，再求二次函数的最大值.解：（1）该商场销售家电的总收益为800 200160000（元）；（2）依 题 意 可 设1800yk x，2200Zk x，有14008001200k，2200200160k，解得12115kk，所以800yx，12005Zx（3）1(800)2005WyZxx21(100)1620005x，政府应将每台补贴款额x定为 100 元，总收益有最大值，其最大值为162000元说明：本题中有两个函数图像，在解题时要结合起来思考，不可顾此失彼.例 2凯里市某大型酒店有包房100 间，在每天晚餐营业时间，每间包房收包房费100元时，包房便可全部租出；若每间包房收费提高20 元，则减少10 间包房租出，若每间包房收费再提高20 元，则再减少10 间包房租出，以每次提高20 元的这种方法变化下去.（1）设每间包房收费提高x（元），则每间包房的收入为y1（元），但会减少y2间包房租出，请分别写出y1、y2与 x 之间的函数关系式.（2）为了投资少而利润大，每间包房提高x（元）后，设酒店老板每天晚餐包房总收入为 y（元），请写出y 与 x 之间的函数关系式，求出每间包房每天晚餐应提高多少元可获得最大包房费收入，并说明理由.分析：（1）提价后每间包房的收入原每间包房收包房费+每间包房收包房提高费，包房减少数每间包房收包房提高费数量的一半；（2）酒店老板每天晚餐包房总收入提价后每间包房的收入每天包房租出的数量，得到二次函数后再求y 取得最大值时x 的值.解：（1）xy1001，xy212；（2）)21100()100(xxyy11250)50(212x，因为提价前包房费总收入为 100 100=10000，当 x=50 时，可获最大包房收入11250 元，因为 1125010000 又因为每次提价为20 元，所以每间包房晚餐应提高40 元或 60 元.说明：本题的答案有两个，但从“投资少而利润大”的角度来看，因尽量少租出包房，所以每间包房晚餐应提高60 元应该更好.例 3某水产品养殖企业为指导该企业某种水产品的养殖和销售，对历年市场行情和水产品养殖情况进行了调查调查发现这种水产品的每千克售价1y（元）与销售月份x（月）文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8满足关系式1y36x83，而其每千克成本2y（元）与销售月份x（月）满足的函数关系如图所示（1）试确定bc、的值；（2）求出这种水产品每千克的利润y（元）与销售月份x（月）之间的函数关系式；（3）“五一”之前，几月份出售这种水产品每千克的利润最大？最大利润是多少？分析：（1）将点（3，25），（4，24）代入求b、c 的值；（2）y1y-2y；（3）将（2）中的二次函数配方为顶点式，再利用二次函数的增减性，在满足“五一”之前的前提下求最大值.解：（1）由题意：22125338124448bcbc，解得7181292bc；（2）12yyy23115136298882xxx21316822xx；（3）21316822yxx2111(1236)46822xx21(6)118x.108a，抛物线开口向下在对称轴6x左侧y随x的增大而增大由题意5x，所 以 在4月 份 出 售 这 种 水 产 品 每 千 克 的 利 润 最 大 最 大 利 润211(46)111082（元）说明：本题在x 6，即 6 月份时取得最大值，但题目要求在“五一”之前，所以要将二次函数配方为顶点式，利用二次函数的增减性来求解.例 4.某商场以每件30元的价格购进一种商品，试销中发现这种商品每天的销售量m(件)与每件的销售价x(元)满足一次函数1623,3054mxx(1)写出商场卖这种商品每天的销售利润y与每件销售价x之间的函数关系式；(2)若商场要想每天获得最大销售利润，每件商品的售价定为多少最合适？最大销售利润为多少？25 24 y2（元）x（月）1 2 3 4 5 6 7 8 9 10 11 122218yxbxcO 文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8解：(1)由已知得每件商品的销售利润为(30)x元，那么m件的销售利润为(30)ym x，又1623mx2(30)(1623)32524860,3054yxxxxx(2)由(1)知对称轴为42x，位于x的范围内，另抛物线开口向下当42x时，2max342252424860432y当每件商品的售价定为42 元时每天有最大销售利润，最大销售利润为432 元二次函数求最值(面积最值问题)例 1.在矩形 ABCD 中，AB=6cm，BC=12cm，点 P 从点 A 出发，沿 AB 边向点 B 以 1cms的速度移动，同时点Q 从点 B 出发沿 BC 边向点 C 以 2cms 的速度移动，如果P、Q 两点同时出发，分别到达B、C 两点后就停止移动（1）运动第t 秒时，PBQ 的面积 y(cm2)是多少？（2）此时五边形APQCD 的面积是S(cm2)，写出 S 与 t 的函数关系式，并指出自变量的取值范围（3）t 为何值时s 最小，最小值时多少？答案：6336333607266126262621)1(2222有最小值等于时；当）（）（）（）（）（）（SttStttttStttty例 2.小明的家门前有一块空地，空地外有一面长10 米的围墙，为了美化生活环境，小明的爸爸准备靠墙修建一个矩形花圃，他买回了32 米长的不锈钢管准备作为花圃的围栏，为了浇花和赏花的方便，准备在花圃的中间再围出一条宽为一米的通道及在左右花圃各放一个1米宽的门（木质）花圃的长与宽如何设计才能使花圃的面积最大？解：设花圃的宽为x米，面积为S平方米则长为：xx4342432(米)则：)434(xxSxx3 4424289)417(42xx文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8104340 x2176x6417，S与x的二次函数的顶点不在自变量x的范围内，而当2176x内，S随x的增大而减小，当6x时，604289)4176(42maxS(平方米)答：可设计成宽6米，长 10 米的矩形花圃，这样的花圃面积最大例 3.已知边长为4 的正方形截去一个角后成为五边形ABCDE（如图），其中 AF=2，BF=1 试在 AB 上求一点 P，使矩形PNDM 有最大面积解：设矩形 PNDM 的边 DN=x，NP=y，则矩形 PNDM 的面积 S=xy（2x4）易知 CN=4-x，EM=4-y 过点 B 作 BH PN 于点 H 则有 AFB BHP PHBHBFAF，即3412yx，521xy，xxxyS5212)42(x，此二次函数的图象开口向下，对称轴为x=5，当 x5时，函数值y随x的增大而增大，对于42x来说，当x=4 时，12454212最大S【评析】本题是一道代数几何综合题，把相似三角形与二次函数的知识有机的结合在一起，能很好考查学生的综合应用能力同时，也给学生探索解题思路留下了思维空间例 4.某人定制了一批地砖，每块地砖（如图(1)所示）是边长为0.4 米的正方形ABCD，点 E、F 分别在边BC 和 CD 上，CFE、ABE 和四边形AEFD 均由单一材料制成，制成 CFE、ABE 和四边形AEFD 的三种材料的每平方米价格依次为30 元、20 元、10 元，若将此种地砖按图(2)所示的形式铺设，且能使中间的阴影部分组成四边形EFGH(1)判断图(2)中四边形EFGH 是何形状，并说明理由；(2)E、F 在什么位置时，定制这批地砖所需的材料费用最省？解：(1)四边形 EFGH 是正方形图(2)可以看作是由四块图(1)所示地砖绕C 点按顺(逆)时针方向旋转90 后得到的，故 CE=CF=CG CEF 是等腰直角三角形因此四边形EFGH 是正方形文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8(2)设 CE=x,则 BE=0.4x，每块地砖的费用为y 元那么：y=x 30+0.4 (0.4-x)20+0.16-x-0.4 (0.4-x)10)24.02.0(102xx3.2)1.0(102x)4.00(x当 x=0.1 时，y 有最小值，即费用为最省，此时CE=CF=0.1答：当 CE=CF=0.1 米时，总费用最省文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ4T10T9B8W7 HY9C5V2D3L3 ZS2N1W5A2B8文档编码:CZ